I dont know if this is actually transmitting over the serial
It is. Whether it is sending it to the serial port that the Arduino is connected to, or not, is a different question.
Serial.list() is a method that returns a list of serial ports that the Arduino MIGHT be connected to. Print that list, to see what is in position 0, to confirm that it is indeed the port that the Arduino is connected to.
that might be too large an assumption
Indeed it is.
Hopefully this will allow me to take this relative mouse movement to the next level!
What is the Arduino going to do with the information about where the mouse is on the PC screen?